Heat 1 tablespoon olive oil in a skillet over medium heat. Once the oil is hot, add the 3/4 cup red bell pepper and 1/2 cup onion. Cook for a few minutes until crisp, tender and remove from the heat.
Use a pastry brush to coat the grill pan or grill grates with a little bit of olive oil, and heat it over medium to high heat. Once the grill is hot, place a tortilla on the grill and cover one-half of the tortilla with cheddar cheese.
Place a layer of bell peppers on top of the cheese, then a layer of shredded chicken then a little more cheese.
Fold over the tortilla and cook for 3 to 5 minutes. Flip the folded tortilla over and cook for a few minutes longer.